Resolution-enhanced quantitative phase imaging from transport of intensity equation: mixed-transfer-function

Transport of intensity equation (TIE) is an established quantitative phase imaging (QPI) method as a deterministic phase retrieval algorithm derived from paraxial approximation. However, this approximation limits TIE to retrieve high-resolution QPI for most biological samples. It can be overcome via the phase transfer function (PTF) method (no paraxial approximation), while it has incorrect phase in low-frequency due to the weak phase approximation. For the general microscopic specimens with thickness and small details, we present a resolution-enhanced QPI mixed-transfer-function (MTF) approach based on the spatial domain and the spatial frequency one, using phase space theory as a bridge. It is proved that the traditional TIE can obtain the accurate phase in low-frequency, but suffers from attenuation and blurring at high frequencies. Thus, MTF is combined with PTF to improve the maximum resolution that can be accurately reconstructed. Simulation results and experiments demonstrate that MTF can achieve high-contrast and high-resolution QPI correctly over the whole theoretical bandwidth, showing efficiency for phase retrieval even in slowly varying large phase objects. Besides, it is compatible with commercial microscopes without additional hardware modification, offering a flexible and cost-effective alternative for biomedical research and cellular investigations.